Fast statistical analysis of process variation effects using accurate PLL behavioral models

Using the behavioral model of a circuit to perform behavioral Monte Carlo simulation (BMCS) is a fast approach to estimate performance shift under process variation with detailed circuit responses. However, accurate Monte Carlo analysis results are difficult to obtain if the behavioral model is not accurate enough. Therefore, this paper proposes to use an efficient bottom-up approach to generate accurate process-variation-aware behavioral models of CPPLL circuits. Without blind regressions, only one input pattern in the extraction mode sufficiently obtains all required parameters in the behavioral model. A quasi-SA approach is also proposed to accurately reflect process variation effects. Considering generic circuit behaviors, the quasi-SA approach saves considerable simulation time for complicated curve fitting but still keeps estimation accuracy. The experimental results demonstrate that the proposed bottom-up modeling flow and quasi-SA equations provide similar accuracy as in the RSM approach, using less extraction cost as in the traditional sensitivity analysis approach.